Since the security problem IE had I've been using Opera Next v22 .
It is a Chrome bases browser & has both Adobe shockwave & flash players.
No problems with it.
What OS ?
My main OS on my desktop is Vista so it uses IE9.
On my laptop with W7 I have IE11.
I don't have FF installed .
Let me know which is closest to the OS & IE you are using & I will give YouTube a test.
Also if you could post a link to a YouTube video you can't play.